Many fitness tests have been created as a unit of measure of various fitness categories, such as general fitness, aerobic fitness, muscular strength, muscular endurance, flexibility, and body composition. The tests are only as accurate as you make them, so reading instructions carefully, and performing them often, should bring more accurate results. Although the tests are only likely to highlight what you already suspect - a bodybuilder achieving "excellent" muscular strength test results, or a marathon runner displaying an "excellent" score for their aerobic fitness tests - it can be used for trend analysis, which can identify progression or decline and might, in turn, alter the way you train your client. Also, it'd be ignorant to assume you've taken all factors into account. Although unlikely, sometimes the test results can throw up a surpise, such as a powerlifter with poor grip strength or an outwardly healthy individual with high blood pressure.
If you're performing these fitness tests on a client for the first time, you should have their full approval and a completed PAR-Q (health questionaire) that you're happy with. If you're working with a deconditioned individual, as a matter of course, they should see their Doctor beforehand and, thereafter, it would prudent to perform the static fitness assessments (measuring general fitness) first.
To re-cap: Static Fitness Tests - those measuring general fitness, good health & well-being. Dynamic Fitness Tests - aerobic fitness, muscular strength, muscular endurance, flexibility.